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2012 | 10 | 4 | 1280-1291
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Derived category of toric varieties with small Picard number

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EN
Abstrakty
EN
This paper aims to construct a full strongly exceptional collection of line bundles in the derived category D b(X), where X is the blow up of ℙn−r ×ℙr along a multilinear subspace ℙn−r−1×ℙr−1 of codimension 2 of ℙn−r ×ℙr. As a main tool we use the splitting of the Frobenius direct image of line bundles on toric varieties.
Wydawca
Czasopismo
Rocznik
Tom
10
Numer
4
Strony
1280-1291
Opis fizyczny
Daty
wydano
2012-08-01
online
2012-05-31
Twórcy
autor
Bibliografia
  • [1] Batyrev V.V., On the classification of smooth projective toric varieties, Tohoku Math. J., 1991, 43(4), 569–585 http://dx.doi.org/10.2748/tmj/1178227429
  • [2] Beilinson A.A., Coherent sheaves on ℙn and problems of linear algebra, Funct. Anal. Appl., 1978, 12(3), 214–216 http://dx.doi.org/10.1007/BF01681436
  • [3] Bondal A.I., Representations of associative algebras and coherent sheaves, Math. USSR-Izv., 1990, 34(1), 23–42 http://dx.doi.org/10.1070/IM1990v034n01ABEH000583
  • [4] Bondal A.I., Derived categories of toric varieties, In: Convex and Algebraic Geometry, Oberwolfach, January 29–February 4, 2006, Oberwolfach Rep., 2006, 3(5), 284–286
  • [5] Bondal A., Orlov D., Derived categories of coherent sheaves, In: Proceedings of the International Congress of Mathematicians, 2, Beijing, August 20–28, 2002, Higher Education Press, Beijing, 2002, 47–56
  • [6] Costa L., Miró-Roig R.M., Tilting sheaves on toric varieties, Math. Z., 2004, 248(4), 849–865 http://dx.doi.org/10.1007/s00209-004-0684-6
  • [7] Costa L., Miró-Roig R.M., Derived categories of projective bundles, Proc. Amer. Math. Soc., 2005, 133(9), 2533–2537 http://dx.doi.org/10.1090/S0002-9939-05-07846-9
  • [8] Costa L., Miró-Roig R.M., Frobenius splitting and Derived category of toric varieties, Illinois J. Math., 2010, 54(2), 649–669
  • [9] Costa L., Miró-Roig R.M., Derived category of fibrations, Math. Res. Lett., 2011, 18(3), 425–432
  • [10] Fulton W., Introduction to Toric Varieties, Ann. of Math. Stud., 131, Princeton University Press, Princeton, 1993
  • [11] Funch Thomsen J., Frobenius direct images of line bundles on toric varieties, J. Algebra, 2000, 226(2), 865–874 http://dx.doi.org/10.1006/jabr.1999.8184
  • [12] Gorodentsev A.L., Kuleshov S.A., Helix theory, Mosc. Math. J., 2004, 4(2), 377–440
  • [13] Hille L., Perling M., Exceptional sequences of invertible sheaves on rational surfaces, Compos. Math., 2011, 147(4), 1230–1280 http://dx.doi.org/10.1112/S0010437X10005208
  • [14] Kapranov M.M., On the derived category of coherent sheaves on Grassmann manifolds, Math. USSR-Izv., 1985, 24(1), 183–192 http://dx.doi.org/10.1070/IM1985v024n01ABEH001221
  • [15] Kapranov M.M., On the derived categories of coherent sheaves on some homogeneous spaces, Invent. Math., 1988, 92(3), 479–508 http://dx.doi.org/10.1007/BF01393744
  • [16] Kawamata Y., Derived categories of toric varieties, Michigan Math. J., 2006, 54(3), 517–535 http://dx.doi.org/10.1307/mmj/1163789913
  • [17] King A., Tilting bundles on some rational surfaces, preprint available at http://www.maths.bath.ac.uk/~masadk/papers/
  • [18] Kuznetsov A.G., Derived category of Fano threefolds, Proc. Steklov Inst. Math., 2009, 264(1), 110–122 http://dx.doi.org/10.1134/S0081543809010143
  • [19] Lason M., Michałek M., On the full, strongly exceptional collections on toric varieties with Picard number three, Collect. Math., 2011, 62(3), 275–296 http://dx.doi.org/10.1007/s13348-011-0044-x
  • [20] Oda T., Convex Bodies and Algebraic Geometry, Ergeb. Math. Grenzgeb., 15, Springer, Berlin, 1988
  • [21] Orlov D.O., Projective bundles, monoidal transformations, and derived categories of coherent sheaves, Russian Acad. Sci. Izv. Math., 1993, 41(1), 133–141
  • [22] Samokhin A., Some remarks on the derived categories of coherent sheaves on homogeneous spaces, J. Lond. Math. Soc., 2007, 76(1), 122–134 http://dx.doi.org/10.1112/jlms/jdm038
Typ dokumentu
Bibliografia
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bwmeta1.element.doi-10_2478_s11533-012-0060-4
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